You wrote down the frequency of precession (from the z axis to -z and back to +z) in terms of B1. Now write the frequency in terms of period (time) [itex]f_1=1 / t_1 [/itex] for one cycle. What fraction of one cycle is the journey from the z axis to the xy plane?

You wrote down the frequency of precession (from the z axis to -z and back to +z) in terms of B1. Now write the frequency in terms of period (time) [itex]f_1=1 / t_1 [/itex] for one cycle. What fraction of one cycle is the journey from the z axis to the xy plane?

I'm not quite sure what you meant ..
So basically I have ω = γB1 = 2∏f1 formula, and if I write this in terms of period it would be like
ω = γB1 = 2∏(1/t).. and I'm lost afterwards.. could you be kind to explain more in detail?

You now have [itex]t_1(360)[/itex] in terms of B1. I've written it with the argument 360 because this period is the length of time for the spin to precess from the z direction down to the xy plane, on to -z, back to the xy plane, and back up to z, for a total angle of 360 degrees. You want the time it takes to go from z to the xy plane, which is an angle of 90 deg. You have everything needed to find that value.